Peaks above the Harrison-Zel’dovich spectrum due to the Quark-Gluon to Hadron Transition

We investigate the effect of the quark-gluon to hadron transition at T⋆ ∼ 150 MeV on the evolution of primordial cosmological perturbations, in particular distortions of the HarrisonZel’dovich spectrum. If the phase transition is first order, the sound velocity vanishes during the transition. Thus, density perturbations fall freely for about a Hubble time. The primordial Harrison-Zel’dovich rms density fluctuations for scales below the Hubble radius at the transition develop peaks and dips, which grow linearly with the wavenumber, both for the hadron-photonlepton fluid and for cold dark matter. The large peaks in the spectrum may affect primordial black hole formation, big bang nucleosynthesis, and they produce cold dark matter clumps of 10 to 10M⊙. QCD makes a confinement transition from a quark-gluon plasma (QGP) at high temperatures to a hadron gas (HG) at low temperatures. Lattice QCD simulations show that this transition takes place at a temperature T⋆ ∼ 150 MeV and give indications that this is a first-order phase transition for the physical values of the u,d,s-quark masses [1]. The relevance of the QCD transition for cosmology, especially for big-bang nucleosynthesis [2], has been discussed before, but the focus was on the effects of bubble formation [3, 4]. In this paper we look at the properties of matter averaged over scales λ much larger than the bubble size and the bubble separation. We show that for a first order phase transition the sound speed cs = (∂p/∂ρ) 1/2 s drops to zero suddenly at the moment the transition temperature T⋆ is reached, stays zero for the entire time until the phase transition is completed, and Seminar presented by C. S. at the Center for Particle Astrophysics, Berkeley (February ’96), Fermi National Lab. (March ’96) and at the ‘Journées Relativistes’ in Ascona, Switzerland (May ’96). 2 e-mail: chschmid, dschwarz, widerin, all @itp.phys.ethz.ch